Simultaneous macroscale and microscale wave–ion interaction in near-earth space plasmas

Identifying how energy transfer proceeds from macroscales down to microscales in collisionless plasmas is at the forefront of astrophysics and space physics. It provides information on the evolution of involved plasma systems and the generation of high-energy particles in the universe. Here we report two cross-scale energy-transfer events observed by NASA’s Magnetospheric Multiscale spacecraft in Earth’s magnetosphere. In these events, hot ions simultaneously undergo interactions with macroscale (~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{5}$$\end{document}105 km) ultra-low-frequency waves and microscale (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim {10}^{3}$$\end{document}~103 km) electromagnetic-ion-cyclotron (EMIC) waves. The cross-scale interactions cause energy to directly transfer from macroscales to microscales, and finally dissipate at microscales via EMIC-wave-induced ion energization. The direct measurements of the energy transfer rate in the second event confirm the efficiency of this cross-scale transfer process, whose timescale is estimated to be roughly ten EMIC-wave periods about (1 min). Therefore, these observations experimentally demonstrate that simultaneous macroscale and microscale wave-ion interactions provide an efficient mechanism for cross-scale energy transfer and plasma energization in astrophysical and space plasmas.

velocity became large. Did the anisotropy in the plasma rest frame also fluctuate with the ULF wave? If this understanding is correct, "anisotropy" in the text and figures should be replaced by "flux ratio". The "flux ratio" can be interpreted as anisotropy, only in cases when the E × B drift energy is negligible. This is the case for high-energy range and/or light ions (for example, hot H + ).

Comment 4
Supplementary Material, Lines 183-189: There are difficulties in calibration of the electric field data, especially the phase (and amplitude) of Ewave, because the response (phase rotation and sensitivity) of the electric field probes is affected by conditions of the surrounding plasma. Have you checked that the phase difference between Bwave and Ewave is 90°? If there is an offset from 90°, how much does it affect the calculations of energy transfer, and have you checked to ensure that it does not change your conclusions? (About the amplitude, comparison between the estimated phase velocity and the ratio between Ewave and Bwave will be useful for validation.)

Comment 5
Supplementary Material, Lines 183-189: I understand that the He + velocity vectors are calculated in the spacecraft rest frame. Since this is the period when the E × B drift due to low-frequency (below the frequency of EMIC waves) electric fields is not small, it may be necessary to subtract the E × B drift velocity from the He + velocity vectors. As discussed in Comment 1, the difference in the frame has a large effect on the velocity vector (phase and magnitude) for the low-energy component. Since the component that was transferring energy to the EMIC wave was relatively low energy, any check seems to be necessary.

Comment 1
Lines 20, 21, 99, 100: What do the scales of the ULF and EMIC waves (~10 5 and 10 3 km) mean? Since the wavelength of the EMIC wave was estimated as 2700 km, I think that they might mean the wavelength. If so, is it possible to say anything about the wavelength of the ULF wave from the observations? For example, Kitamura et al. (2021, JGR, https://doi.org/10.1029/2020JA028912) estimated a wavelength of ULF waves as ∼ 3600-9000 km using the data obtained by the MMS spacecraft, although the wavelength is much smaller than 10 5 km. If the wavelength was very long, no difference must be visible between the spacecraft. If so, I think that you can write that. Since the scales are important in this manuscript, it is good to define and demonstrate the scales as carefully as possible.

Comment 2
Line 50: Since this is a magnetospheric phenomenon, to show the spacecraft location in the magnetic latitude, magnetic local time, and L-value coordinate in addition to that in the GSE coordinates is useful for readers. Since it is a bit far from the Earth, I think that it is good to also add information about the distance and relative location (north or south) This work is clearly of publishable standard and has been extensively reviewed and updated already. It does reveal evidence for an energy cascade between larger scale ULF waves and smaller scale EMIC waves through use of the high time resolution and small spatial scale of the MMS array. This cross-scale energy transfer is important as it enables a fast and efficient mechanism for plasma energization.
We thank the reviewer for carefully reading the manuscript and making constructive comments. As suggested by the reviewer, we have revised the manuscript by adding a new event that shows the same mechanism operates. The observations are summarized in Fig. 1. Related discussions can be found in lines 59-100.
In the new event, the cross-scale energy transfer processes are caused by the cross-scale interactions of H + ions, ULF waves and EMIC waves. Here we chose an event in which H + ions are involved (rather than He + ions as in the old event), because we want to make a point that both the major and minor species of plasmas can mediate cross-scale wave-particle interactions and thus cross-scale energy transfer processes. Except for particle species, the overall mechanism in the new event is the same as the old event: First, the ULF waves (Fig.  1a) quasi-periodically accelerate 9.8-27 keV H + ions (Fig. 1b-c) and increase their anisotropy (Fig. 1g), and then, the resulting anisotropic H + ions quasi-periodically excite/amplify the EMIC waves (comparing Fig. 1g and Fig. 1f), leading to the control of the EMIC waves by the ULF waves (Fig. 1h). Besides the new event described above, we have also found another six similar events (see Supplementary Table 1). Unfortunately, no burst mode data is available in all of these events (including the above one). As a result, we cannot analyze the energy transfer processes in these events in detail. It is very hard to find events in which cross-scale wave-particle interactions and burst mode data are simultaneously available. Actually, this is why we concentrate on the 2019/01/07 event, even though it has been reported before (but for very different purposes). Nevertheless, another seven events have been found, indicating cross-scale wave-particle interaction events are not rare. Future studies can provide us with more findings.
It seems the issue that has been pointed out is that although the measurements have unique accuracy, such cross-scale coupling processes have been shown (or conjectured) before, although it is not clear that previously such a complete and direct determination has been done (as is possible with the 4 spacecraft measurements). A second issue raised by referee3, however, is that the present paper follows the analysis of the same event as considered by Shi et al (2020), which undoubtedly it does, and indeed some aspects of the ion modulation by both EMIC and Pc5 (ULF) waves were pointed out by Shi et al.
We agree that such cross-scale coupling processes have been conjectured before. However, we suggest that our studies, for the first time, give direct, observational and quantitative evidence for the processes and their importance (both with the four spacecraft measurements and the direct measurements of ion gyration).
We also would like to compare our studies with Shi et al. briefly here. Indeed, Shi et al. and our studies investigate the same event. However, the main focus of Shi et al. is the behavior (or more precisely, the × drift) of cold H + ions (<50 eV) in EMIC waves and ULF waves, whereas our studies concentrate on the resonant interactions of hot (>200 eV) He + ions, ULF waves and EMIC waves, and the resulting cross-scale energy transfer processes. None of our results is discussed in Shi et al.. Shi et al. and our studies investigate the same event but for entirely different purposes.
The authors have refuted these claims and argue that their treatment is a substantial extension of that of Shi et al to show new results not considered there. I do accept that substantially more is done in the present paper, in particular on the wave coupling and amplification, but I feel this is still an extension and further interpretation of results already noted, albeit a significant one. It probably is for the editors to make a final decision as to whether this is substantial enough to warrant publication in Nature Communications. In case the answer is negative, however, I think one way the authors could provide an improvement that would potentially allow publication, would be to demonstrate one other event that shows that the same mechanism operates. In that case, I feel there would be little argument against publication in NatComm.
Referee1 points out that the importance of the cold ion population could be shown in other situations, and in response the authors admit that more events are needed, although they feel this study should inspire further analysis. Again, a second event would go a long way towards nailing down this point. Most of the technical issues the referee raises appear to be answered by the authors.
Again, thanks very much for the comments. The manuscript has been revised accordingly. Please find the detailed response above.
Referee2 comments that other work has discussed some of these aspects and points out that Kitamura et al. has performed similar analysis with MMS using similar techniques. The authors claim that their analysis in the present paper produces unambiguous evidence for the mechanisms, but they don't explain why the previous studies were ambiguous using the same dataset. I feel that the present paper does connect some of the different aspects and interplay of instabilities in a more complete way than the previous studies have hinted at. However, I can only repeat that a second event showing the same balance of processes would be hugely convincing. Given the inspiring nature of this work, that might not be an onerous thing for the authors to try.
We agree that our paper gives a more complete investigation of the different aspects and interplay of instabilities. We sincerely appreciate your positive comment. cyclotron-resonance, whereas ours is cross-scale energy transfer processes mediated by cross-scale wave-particle interactions. Indeed, in terms of the EMIC wave-ion interactions, there are some overlaps between Kitamura et al. and our studies. However, we two focus on very different topics.
From my point of view, I accept that the present paper does build on previous work and has revealed a plausible scenario for how the coupling operates. However, I feel they would solidify this scenario by analysis of at least one other event. I feel the comments by the three referees are not unreasonable, but the authors have made efforts to make corrections to most of the technical queries. Whether these clarifications alone are sufficient to allow publication in Nature Communications is perhaps up to the editors.
We would like to express our gratitude to the reviewer again. The manuscript has been revised accordingly. Please find the details in the new version of the manuscript.
Reviewer #2 (Remarks to the Author): The authors have addressed most of my comments and expanded on their original analysis.
We sincerely appreciate the constructive comments from the reviewer and have revised the manuscript accordingly. Please find our responses to the comments below.
There are still a couple points that I find unclear. First, the Bx field measurements in Figure 1b do not show a correlation between EMIC waves packets and ULF wave phase; they look pretty random. There is no one-to-one correspondence between the ULF wave oscillations in panel 1b and the flux oscillations in panel 1c, either. What is the correlation coefficient between these time series? And what are the criteria for modulation applied here?
Thanks very much for the comments. There is a good correlation between the EMIC wave packets and the ULF wave phase, and the oscillations in panel 2b and panel 2c (Please note that Fig. 2 in the revised manuscript corresponds to Fig. 1

in the old version).
For the correlation between the EMIC wave packets and the ULF wave phase. First of all, please note that the ULF waves in this event are most clearly manifested as electric field oscillations rather than magnetic field oscillations. This phenomenon, which is frequently reported in the literature, could be attributed to the odd harmonic standing wave structures of ULF waves, as the spacecraft are located near the magnetic equator in this event. Thus, it would be better to investigate the correlation between the EMIC wave packets and the ULF wave electric fields rather than magnetic fields. Supplementary Fig. 2d (and Fig. R1a attached below) shows the corresponding correlation coefficient, which is derived from a cross-wavelet analysis [Grinsted et al., 2004]. It is clear that a correlation coefficient as high as ~0.7 is reached at the periods of ~4-6 minutes, which is also approximately the periods of the ULF waves and EMIC wave packets. This correlation coefficient suggests that there is a good correlation between the EMIC wave packets and the ULF wave phase. This is also the criteria for modulation applied. Please find the related discussions in lines 156-158 in the revised manuscript.
For the second part of the comments. Fig. R1b attached below gives the cross-wavelet correlation coefficient between the ULF wave oscillations in Fig. 2b and the flux oscillations in Fig. 2c. We can see that, at the periods of ~4-6 minutes, the correlation coefficient is as high as ~1, indicating a good correlation between the two flux oscillations. Further, we also calculate the correlation coefficient between the ULF wave electric fields and the flux oscillations in Fig. 2c, and show the results in Fig. R2c. Again, a high correlation coefficient of ~0.8 is reached at the periods of ~4-6 minutes. These results conclude that there is a good correlation between the ULF wave oscillations in Fig. 2b and the flux oscillations in Fig. 2c. Second, the authors state that ULF waves quasi-periodically increase the PSD and anisotropy of 200-600 eV He+ ions and the resulting anisotropic He+ ions quasi-periodically amplify initially small amplitude EMIC waves via the ion cyclotron anisotropy instability. However, it is not demonstrated using the linear theory whether the low-density 200-600 eV He+ suggested as the energy source provides enough free energy for positive EMIC wave growth. In other words, whether the He+ plasma beta and temperature anisotropy are close to or exceed the EMIC instability threshold. The instability analysis has been done by e.g., Kennel andPetschek, 1966 andBlum et al., 2009. Consequently, is 0.14, 0.11 and 0.19. We can see that, is greater than in the first and third time intervals. In the second time interval, though is a little smaller, it is still close to . These results suggest that the hot He + ions considered indeed can provide enough free energy for positive EMIC wave growth. Discussions of this point have been added to the manuscript. Please find lines 176-184 in the revised manuscript.
Overall, due to the similarities with other published studies (previously discussed), I believe this manuscript would be more suitable for a more specialized journal, for example, Geophysical Research Letters or Journal of Geophysical Research. The science advances presented here are rather incremental to justify publication in Nature Communications, though would be of interest to the magnetospheric community once the paper is revised.
Again, we sincerely appreciate the referee for spending time reviewing this manuscript.

Respectfully, we still suggest that our studies are very different from other publications (both Shi et al. and Kitamura et al.). We concentrate on cross-scale energy transfer processes mediated by cross-scale wave-particle interactions, whereas Shi et al. focus on cold H + ion behavior in EMIC waves and Kitamura et al. focus on EMIC wave-ion cyclotron resonance.
There are indeed some overlaps, but our purposes are entirely different. In addition, we have made many further revisions to the new version of the manuscript. Especially, besides addressing all the technical issues, a new event that shows the same mechanism operates is included in the revised manuscript ( Fig. 1 and lines 59-100). Therefore, based on the new expansions, we would like to ask if the reviewer could reconsider the general comment?
Reviewer #3 (Remarks to the Author): This manuscript addresses interesting observations about cross-scale energy transfer in the magnetosphere using a unique dataset derived by the MMS spacecraft. I understand that the importance of the topic. However, additional justification is needed for acceptance. If it is difficult due to length constraints, it can be included in Supplemental Material.
We are very grateful to the reviewer for the constructive comments. We have given full consideration to the comments and revised manuscript thoroughly. Please find our detailed responses to the comments in the following letter.
Please note that we have included a new event in the revised manuscript (as suggested by reviewer #1). This event shows that the same mechanism can also operate for H + ions. The observations of the new event are summarized in Fig. 1 of the revised manuscript. Related discussions can be found in lines 59-100.
Major Comment 1 Lines 81-84: Although the energy of 400 eV appears to be much greater than the E × B drift energy, it needs to be discussed more carefully. When the E × B drift energy for H+ is 25 eV, the E × B drift energy for He+ becomes 100 eV, which corresponds to the velocity of ~70 km/s. In the E × B drifting frame, additional 70 km/s (30 km/s), which corresponds to the energy of 100 eV (20 eV) for He+, is needed to reach 400 eV (200 eV) in the spacecraft frame. Thus, the energy needed in the E × B drifting frame is much smaller than the energy seen by the spacecraft. Thus, I afraid that the high-energy tail of the warm He+ distribution might affect the enhancement of PSD around a few hundreds of electron volts (seen in the spacecraft frame). Is it possible to rule out such a possibility? Do you think that the (perpendicular) temperature of He+ (in the E × B drifting frame) was much lower than 100 eV (20 eV)? If so, the effect of high-energy tail may be small.  Major Comment 2 Lines 83-87: Is there any evidence that He+ satisfied any drift-bounce resonance condition? If it is difficult to show it, is it possible to show existence of plausible resonance conditions that He+ may be able to satisfy? If even it is difficult, is it possible to show any previous studies that such low-energy ions were accelerated by the drift-bounce resonance? I think that such discussion is necessary to reject the possibility mentioned in Comment 1. (As another possibility, the EMIC wave itself may heat He+ in the perpendicular direction (non-locally?) and an excess energy may be returned to the waves at the position of the spacecraft. In such a case, ULF waves may not affect the energy transfer. It would be better to have some stronger evidence of the drift-bounce resonance to rule out such a possibility.) Thanks very much for the helpful comments. First of all, we have to admit that there is no more direct evidence for the drift-bounce resonance between the ULF waves and the He + ions. A major obstacle here is that we cannot accurately determine the azimuthal wavenumber ( ) and the standing wave structures of the ULF waves, which is a problem frequently met in ULF wave-particle interaction studies. Please note that, in this event, the separation among the four MMS spacecraft is too small to accurately determine via a timing method. Regarding the second part of this comment, we suggest that it is hard to apply the non-local EMIC wave-ion interaction scenario here. Please note that there is a good correlation between the He + PSD enhancements (Fig. 2c) and the ULF wave-induced E×B drift arcs (Fig.  2b). This good correlation suggests that, as the case for the latter, the former should also be caused by the ULF waves. The ULF wave-ion-EMIC wave interaction scenario proposed in our manuscript can give a comprehensive explanation of all the observations, which cannot be done easily by the non-local EMIC wave-ion interactions scenario, although it is possible in principle.

Major Comment 3
Lines 107-110: If my understanding is correct, the "anisotropy" is calculated in the spacecraft rest frame. Anisotropy should be calculated in the plasma rest frame (~the E ×B drifting frame). I afraid that the "anisotropy" was overestimated when E × B drift velocity became large. Did the anisotropy in the plasma rest frame also fluctuate with the ULF wave? If this understanding is correct, "anisotropy" in the text and figures should be replaced by "flux ratio". The "flux ratio" can be interpreted as anisotropy, only in cases when the E × B drift energy is negligible. This is the case for high-energy range and/or light ions (for example, hot H+).
Thanks very much for identifying this issue. Indeed, the "anisotropy" in the previous version is calculated in the rest frame of the spacecraft. Now, in the revised manuscript, the anisotropy is calculated in the rest frame of the plasma. As you can see in Supplementary Fig.  1, the new anisotropy is very similar to the old one and also oscillate with the ULF waves. Therefore, our conclusions still hold.

Major Comment 4
Supplementary Material, Lines 183-189: There are difficulties in calibration of the electric field data, especially the phase (and amplitude) of Ewave, because the response (phase rotation and sensitivity) of the electric field probes is affected by conditions of the surrounding plasma. Have you checked that the phase difference between Bwave and Ewave is 90°? If there is an offset from 90°, how much does it affect the calculations of energy transfer, and have you checked to ensure that it does not change your conclusions? (About the amplitude, comparison between the estimated phase velocity and the ratio between Ewave and Bwave will be useful for validation.)

Thanks very much. In the revised manuscript, we have added a figure showing the phase difference between Bw and Ew (Supplementary Fig. 4e). We can see that the phase difference is roughly + ∘ , with the positive sign indicating anti-parallel propagation (as the waves are left-hand polarized). This result is consistent with our expectations. Supplementary Fig. 4f compares the amplitude of the observed electric fields (blue curve)
and that calculated from ⃗ ⃗ = ⃗ ⃗ × ⃗⃗ (red curve). The observed curve roughly matches the theoretical one. The absolute and relative differences between them are ~0.3 mV/m and ~25%, respectively. Therefore, we suggest that the electric field instruments performed well in this event, ensuring a reliable calculation of the energy transfer between plasma and wave fields.

Materials.
Major Comment 5 Supplementary Material, Lines 183-189: I understand that the He+ velocity vectors are calculated in the spacecraft rest frame. Since this is the period when the E × B drift due to low-frequency (below the frequency of EMIC waves) electric fields is not small, it may be necessary to subtract the E × B drift velocity from the He+ velocity vectors. As discussed in Comment 1, the difference in the frame has a large effect on the velocity vector (phase and magnitude) for the low-energy component. Since the component that was transferring energy to the EMIC wave was relatively low energy, any check seems to be necessary.
Sorry for the confusion, but here the energy gains were calculated in the rest frame of the plasma. Therefore, the contributions from the E×B drift have already been removed. This point is stated more clearly in the revised manuscript. Please find line 318 in the main manuscript and line 243 in the Supplementary Materials.
Minor Comment 1 Lines 20, 21, 99, 100: What do the scales of the ULF and EMIC waves (~105 and 103 km) mean? Since the wavelength of the EMIC wave was estimated as 2700 km, I think that they might mean the wavelength. If so, is it possible to say anything about the wavelength of the ULF wave from the observations? For example, Kitamura et al. (2021, JGR) estimated a wavelength of ULF waves as ∼3600-9000 km using the data obtained by the MMS spacecraft, although the wavelength is much smaller than 105 km. If the wavelength was very long, no difference must be visible between the spacecraft. If so, I think that you can write that. Since the scales are important in this manuscript, it is good to define and demonstrate the scales as carefully as possible.
Thanks for identifying this issue. In this study, the wavelength is used as a proxy for the spatial scales of the waves. Also, no difference is visible between the four MMS spacecraft (both for the ULF waves and the EMIC waves).
Here, the wavelength of the ULF waves is estimated from the dispersion relation for Alfven waves, = ∥ . In this event, the Alfven velocity is ~662 km/s, as the amplitude of the background magnetic field is ~45 nT and the plasma number density is ~2.2 cm -3 . On the other hand, the angular frequency of the ULF waves is about = . rad/s. Thus, the wavelength of the ULF waves is ∥ = . × km. This is why we say that the scale of the ULF waves is on the order of km.
We have added a new subsection titled "Estimating the spatial scales of waves" in the Supplementary Materials. The technical definition of the spatial scale of waves, together with how it is obtained, is given in this subsection. Please find the details in lines 156-164 in the revised Supplementary Materials.
Minor Comment 2 Line 50: Since this is a magnetospheric phenomenon, to show the spacecraft location in the magnetic latitude, magnetic local time, and L-value coordinate in addition to that in the GSE coordinates is useful for readers. Since it is a bit far from the Earth, I think that it is good to also add information about the distance and relative location (north or south) to minimum-B at low latitudes. (The location of minimum-B in the MMS MEC data may be usable.) Thanks. These parameters are now given in lines 103-106.
Minor Comment 3 Lines 92-93: I suggest adding the wave frequency normalized by the cyclotron frequency of H+.
Have done. Please find it in line 152.

Minor Comment 4
Lines 197-198: If my understanding is correct, "besides lower ~" is not come from the present result. To avoid misunderstandings, it would be better to emphasize more that it comes from other results.
Have done. Please find lines 267-268 in the manuscript.
Minor Comment 5 Lines 216-217: What do the curves in Fig. 2b indicate?
The two curves are just used to guide the eyes. They do not indicate anything specially. We have added a brief description in line 316. For all the panels shown in Supplementary Fig. 1, the anisotropy is defined as The color code represents the normalized PSDs, which are defined as ( , , ) ( , , ) , where denotes PSDs, and represent energy and pitch angle (fixed in the normalization processes), respectively, and represents the ith gyrophase channel. As defined in this way, 0% means that the PSDs in this gyrophase channel are zero, and 100% means that the PSDs in other gyrophase channels are zero. We have added a brief description of this point in the manuscript. Please find lines 321-322 in the main manuscript and lines 212-213 in the Supplementary Materials.

Minor Comment 9
Supplementary Material, Lines 120-128: It is necessary to explain why you can ignore He+ (and O+).
Thanks. According to the HPCA observations, the total number density of He + and O + ions are only ~2% and ~1% of that of H + ions, respectively. Thus, to a first order approximation, the heavy ions would not affect the dispersion relation much and thus can be ignored. We

Minor Comment 11
Supplementary Material, Lines 139-143: The description about FPI is incorrect. The energy range does not agree with Fig. 1a (2 eV?-20 keV?). The energy range does not appear to be log-evenly divided at least below 10 eV (Fig. 1b). The use of the two energy tables for the FPI burst data was supposed to have been stopped in 2016. Some description about the fast survey data is also necessary, if they are also used.

Reviewers' comments:
Reviewer #1 (Remarks to the Author): I have read the responses the authors have made and I feel that on balance the paper is essentially ready for publication from my point of view. I feel this study is an important confirmation of the energy cascade processes, despite the fact that some aspects have been reported in other work (but not with the depth of analysis given here). They have made corrections along the lines I suggested (even though I indicated these were optional).
The most important addition is to include a second event which shows that similar processes operate (given the context of slightly different event conditions). The authors also reasonably point out the limitations of the datasets currently available so that other events often do not have the data resolution needed for a full analysis.
The addition of another event shows that the exact nature of the cross-scale transfer depends on input conditions to some extent and I feel this also addresses the criticism that other work has dealt with this topic. In this work, common mechanisms (as well as differences) are shown through an event comparison, as well as utilising high-precision, multi-spacecraft data to give direct evidence, which was not carried out before.
I recommend publication.
Reviewer #2 (Remarks to the Author): The authors have addressed my previous comments and supported their conclusions by extended analysis. However, I still believe this manuscript would be more suitable for a more specialized journal, for example, Geophysical Research Letters or Journal of Geophysical Research as it does not represent "important advances of significance to specialists in the field" to justify publication in Nature Communications.
Reviewer #3 (Remarks to the Author): Regrettably, based on the newly added sections, I have come to suspect that it may be difficult to clearly demonstrate what you are trying to prove in the present manuscript, although I understand the importance of the topic.
Lines are for the text with track changes. , energy transport is probably directed from the ULF waves to ions. Since the events are quiet condition, this would not be the case without any evidence. Thus, the direction of energy transport is at least not obvious. I think that it is impossible to conclude that the ions were accelerated by the ULF waves unless you rule out internal excitation of the ULF wave by ions or show any evidence of energy transport from the ULF waves to the ions. Although I understand that this is a rather difficult requirement, since the main conclusion is the transport of energy from macroscales to microscales, any possibility or idea that contradicts the scenario must be eliminated. Lines 63 and 105: Since it is a bit far from the Earth, I think that it is good to also add information about the distance and relative location (north or south) to minimum-<i>B</i>. (In the outer magnetosphere, 0° in the magnetic latitude in the MMS MEC data does not indicate the location of minimum-<i>B</i>. The location of minimum-B is provided separately in the MEC data.)

Comment 2
Line 316 and Supplementary materials Line 67: I think that the HPCA data used for those figures are in the fast survey mode.

Comment 3
When calculating the rest frame of the plasma for FPI data, it is necessary to make an assumption about ion species. Is it assumed that they are all He+? Furthermore, since EMIC waves cause electric field fluctuation with a short period, it is necessary to be careful in handling the electric field data to determine the rest frame of the plasma. I think that it is good to describe how the rest frame of the plasma was determined for each of the ion measurements with various time resolutions. I have read the responses the authors have made and I feel that on balance the paper is essentially ready for publication from my point of view. I feel this study is an important confirmation of the energy cascade processes, despite the fact that some aspects have been reported in other work (but not with the depth of analysis given here). They have made corrections along the lines I suggested (even though I indicated these were optional).
The most important addition is to include a second event which shows that similar processes operate (given the context of slightly different event conditions). The authors also reasonably point out the limitations of the datasets currently available so that other events often do not have the data resolution needed for a full analysis.
The addition of another event shows that the exact nature of the cross-scale transfer depends on input conditions to some extent and I feel this also addresses the criticism that other work has dealt with this topic. In this work, common mechanisms (as well as differences) are shown through an event comparison, as well as utilizing high-precision, multi-spacecraft data to give direct evidence, which was not carried out before.

I recommend publication.
We are very grateful to reviewer #1 for his/her continued efforts in evaluating this paper.

Reviewer #2 (Remarks to the Author):
The

The question we investigate is that, besides turbulent cascade, could any other processes mediate cross-scale energy transfer in collisionless plasmas? With direct in-situ measurements,
we demonstrate for the first time that the cross-scale interactions between hot ions, macroscale ULF waves, and microscale EMIC waves are such a candidate, since direct energy transfer from macroscales down to microscales can take place via this mechanism. This newly identified "cross-scale wave-particle interaction" mechanism provides a novel basis for understanding cross-scale energy transfer processes in space and astrophysical plasma systems.
In contrast, Kitamura et al. only concentrate on a microscale process, the EMIC wave-ion cyclotron resonance. They neither studied macroscale processes nor cross-scale processes.

Also, we focus on very different physics from Shi et al., although we both analyzed the same event. Shi et al. studied the behavior of cold ions in EMIC wave fields. They neither discussed
nor identified the cross-scale coupling processes controlling the event. Therefore, we are emphatic that our manuscript is entirely different from these two papers.

Reviewer #3 (Remarks to the Author):
Regrettably, based on the newly added sections, I have come to suspect that it may be difficult to clearly demonstrate what you are trying to prove in the present manuscript, although I understand the importance of the topic.
We are very grateful to the reviewer for the constructive comments and the judgment of the importance of our manuscript's topic. We have revised the manuscript according to the comments listed here. Especially, we have calculated the local energy flow between the ULF waves and ions, using the observed electric fields and ion velocity distributions. The results suggest that the energy transport is indeed directed from ULF waves to ions, when EMIC waves are observed. The new results well support our two-step mechanism: The ULF waves first quasi-periodically accelerate hot ions and increase their anisotropy, and then, the anisotropic ions quasi-periodically excite/amplify the EMIC waves. Please see the detailed response below.

Major Comments
Comment 1 Lines 59-100: In this section, you attempt to argue that H + ions are accelerated by the ULF waves.
However, H + ions, inversely, may excite the ULF wave. Tian et al. (2022) and Kitamura et al. (2021) indicate that (mainly) compressional ULF waves may be generated internally by anisotropic ions.
If their expectation is correct, the direction of energy transfer is opposite to what is argued in the present manuscript. The situation seems to be similar to the events studied by them, since there appears to be a significant compressional component in all events, except for the inappropriate events (2 and 5 in Table 1) directed from the ULF waves to ions. Since the events are quiet condition, this would not be the case without any evidence. Thus, the direction of energy transport is at least not obvious. I think that it is impossible to conclude that the ions were accelerated by the ULF waves unless you rule out internal excitation of the ULF wave by ions or show any evidence of energy transport from the ULF waves to the ions. Although I understand that this is a rather difficult requirement, since the main conclusion is the transport of energy from macroscales to microscales, any possibility or idea that contradicts the scenario must be eliminated.
We sincerely appreciate the comments. We totally agree that we cannot identify unambiguously the source of the ULF waves here, because of the lack of necessary information (e.g., radial gradient of ion phase space densities). However, respectfully, we disagree with the suggestion that "the direction of energy transfer is opposite to what is argued in the present manuscript", if the ULF waves are generated internally. In the revised manuscript, we have calculated the local energy flow ( ⋅ ) between the ULF waves and ions, using the in-situ measurements of ULF wave electric fields and ion velocity distributions (from FPI). Figure 1f shows the obtained energy gain per ion per unit time for ions in the energy range of 9.8-26.6 keV. We can see that, when the EMIC waves are observed, the energy flow is directed from the ULF waves to ions (i.e., the energy gain is positive). Thus, the new observations support our scenario.
We note that the mechanism proposed in our manuscript actually does not require any specific sources of ULF waves. It can also happen when ULF waves are internally excited. In this situation, ULF waves are still able to periodically transfer energy to H + ions, increase ion anisotropy and then cause local EMIC wave growth. During the growth of the EMIC waves, part energy irreversibly flows from ions to the EMIC waves, and does not return to the ULF waves anymore. In this way, energy transfer proceeds from macroscales to microscales. Our explanations still match the observations in this situation. The key point here is that the energy exchange between EMIC waves and ions is more localized (both spatially and temporally) than that between the ULF waves and ions. Although the ultimate energy source might be ions, ULF waves can still transfer energy to ions and make the latter act as an energy source of EMIC waves at a given time and location. Nevertheless, regarding our event, we suggest that the actual source of the ULF waves is not an essential issue, since the direct observations show that the energy is flowing from ULF waves to ions, when EMIC waves are observed.
We have added some new discussions in the revised manuscript accordingly. Please find lines However, we have rechecked the data and did not find any such signals. Therefore, in the revised manuscript, we choose to use a more general term, "drift-bounce interactions", instead of the old one, "drift-bounce resonance".
However, we suggest that our conclusions are not affected much. Now, we have calculated the energy flow between the ULF waves and He + ions, using the directly measured electric fields and ion velocity distributions (HPCA fast survey data). As shown in Supplementary Fig. 1c, the results suggest the energy is directed from the ULF waves to He + ions when the three EMIC wave packets are observed. Thus, the new direct measurements support our conclusions that the ULF waves are transferring energy to He + ions, when EMIC waves are observed.

In addition, we suggest that the scenario proposed in our manuscript actually does not require resonant interactions between ULF waves and ions. Without resonance, ULF waves can also accelerate ions in the perpendicular direction, increase their anisotropy to exceed the EMIC wave-instability threshold, and then lead to EMIC wave growth. (Of course, without resonance
and EMIC wave excitation, the energy from ULF waves to ions will fully return to ULF waves in the next half wave cycle.) Thus, our scenario can occur without resonance. Finally, we would like to highlight here that our scenario provides a simple, straightforward but complete explanation for all the various observations: the quasi-periodic perpendicular acceleration of He + ions by ULF waves (Fig. 2c and Supplementary Fig. 1c), the quasi-periodic increase of He + ion anisotropy (Supplementary Fig. 1d and 1e), the EMIC wave packets appearing in coincidence with the ULF wave fields (Figure 2d and Supplementary 2d), the signatures indicative of EMIC wave-ion cyclotron-resonance (Fig. 4), and the secular energy flow directed from ions modulated by ULF waves to EMIC waves (Fig. 4)  to remove the relevant text, and instead only give a more general, qualitative discussion about the instabilities. Our consideration is primarily based on the following reasons. The second reason is that there is no need to seek help from quantitative instability analysis here. As shown in the manuscript, we have already directly observed the energy exchange between the EMIC waves and particles, and find the observed energy exchange is large enough to cover the growth of the EMIC waves (Fig. 4). Thus, unlike in previous studies where direct observations are unavailable, here we can conclude from observations themselves that the hot anisotropic He + ions observed can provide enough free energy for the growth of the EMIC waves.

The first reason is that it is not appropriate to use any linear or quasi-linear instability
Therefore, in accordance with the above argument, we decided to remove the text related to quantitative instability analysis from the manuscript. However, we still give

Comment 3
When calculating the rest frame of the plasma for FPI data, it is necessary to make an assumption about ion species. Is it assumed that they are all He+? Furthermore, since EMIC waves cause electric field fluctuation with a short period, it is necessary to be careful in handling the electric field data to determine the rest frame of the plasma. I think that it is good to describe how the rest frame of the plasma was determined for each of the ion measurements with various time resolutions.
We are grateful for the suggestions. The rest frame of the plasma is used for three figures: Supplementary Fig. 1d-1f, Supplementary Fig. 3 and Fig. 4b. For all the three uses, the frame is determined from direct plasma measurements, rather than electric field data. Now, the working definitions of these frames are given in lines 239-257 in the Supplementary Materials: The rest frame of the plasma is used when calculating the anisotropy of H + and He + ions (Supplementary Fig. 1 and 3), and the energy exchange between He + ions and EMIC waves (Fig. 4b). The working definitions of these frames are: Supplementary Fig. 1. For Supplementary Fig. 1c presenting He + ion anisotropy, the rest frame of the plasma is determined according to the bulk velocity of He + ions given in the HPCA fast survey mode data. For Supplementary Fig. 1e showing H + ions, the rest frame of the plasma is determined according to the bulk velocity of H + ions given in the HPCA fast survey mode data. Supplementary Fig. 3. Here, the rest frame of the plasma is defined according to the He + ion bulk velocity given in the HPCA fast survey mode data. The frame transformation is applied prior to the time average. Comment 5 Table 1 (Line 78): Although Event 2 has burst data, the increase in wave intensity in the frequency range of EMIC waves seems to be caused by contacts with the boundary layer due to the ULF wave. I consider that this event is unsuitable for the present analysis.
We agree with the reviewer. We have removed this event from the table.

REVIEWER COMMENTS
Reviewer #3 (Remarks to the Author): I understand the importance of the topic, and I think that the revision is in the right direction, but the lack of important information in the text makes it impossible to evaluate whether the results are valid or not in the current situation.
Please see my comments below.
I understand the importance of the topic, and I think that the revision is in the right direction, but the lack of important information in the text makes it impossible to evaluate whether the results are valid or not in the current situation.
Lines are for the text with track changes.

Major Comments
Comment 1 Line 73: The definition of the observed ULF-wave electric field (Ew) is not written. Is the component in any frequency range extracted? Excluding the contribution of DC component is important to exclude the effect of non-zero (instrumental or physical) offset.

E = EDC + Ewave vi = vi_DC + vi_wave
Even if the dot product of EDC and vi_DC is zero, the dot product of E and vi is not equal to Ewave and vi_wave (energy transfer between ULF wave components). There may be contributions from the dot products of Ewave and vi_DC or EDC and vi_wave.

Comment 2
Lines 100-102: As discussed in my previous comments, I think that one should not ignore the possibility that the ULF wave is primarily a compressional mode structure. If the ULF wave is mainly compressional mirror-mode like structures (almost zero frequency in plasma rest frame), it seems more correct to say that the energy is transferred gradually as the decay of the structures rather than periodically. If it is not the case, it is only necessary to show that the compressional component was not dominant. I think that it will be more reader-friendly and the physics easier to understand if the electromagnetic field is converted to the field-aligned coordinate system (toroidal, poloidal, and compressional components) in the entire discussion related to the ULF waves. Instead of Fig. 1a, I suggest plotting the three components of the magnetic field variation in the field-aligned coordinates and the three components of the electric field variation (=Ew?) in the field-aligned coordinates with two panels. If there is a possibility that the compressional component was dominant, it seems appropriate to cite a couple of papers on compressional ULF waves (structures) in addition to those on the other modes that have already been cited.
Comment 3 I think that it will help to understand the variation of P if you show not only the electric field (Ew) but also three components of vi in the field-aligned coordinates in Fig. 1 Fig. 1. If the table is kept as it is, I think it will be better to replace the components written in the ULF Field with those in the field-aligned coordinates (toroidal, poloidal, or compressional), and for δEULF→i, the time interval used for the calculation should be indicated in each added figure with the description in the figure caption. It may be worthwhile to add the events treated in the main text to the table.

Comment 5
Since it has changed to treat not only EMIC waves but also ULF waves in detail in this revision, the use of Ew, Ewave, Bwave, and fwave, etc. makes it difficult for readers to understand which wave they are related to. I suggest replacing them with descriptions (e.g., Ew_EMIC or Ew_ULF) that makes it easy to identify immediately which wave they are related to.

Comment 6
Using E for both electric field and energy is confusing. The same is true for the use of f for PSD and frequency. The use of P for energy transfer is also slightly confusing with We agree with the reviewer and are sorry for the confusion. When calculating the ion energy gain ( , ⋅ , ), only components in the period range of 0.25-7 min were included (the lower and higher period limit are about twice the periods of the EMIC waves and the ULF waves, respectively). Both DC and EMIC-wave fields were excluded in the calculation, as now shown by the revised Fig. 1d and 1e.
We have revised the manuscript to show this point directly. Please find lines 70-71: Here, a bandpass filter (0.25-7 min) is used when generating this panel.

and lines 315-316:
When generating panels c-f, a 0.25-7 min bandpass filter has been used.

Comment 2
Lines 100-102: As discussed in my previous comments, I think that one should not ignore the possibility that the ULF wave is primarily a compressional mode structure. If the ULF wave is mainly compressional mirror-mode like structures (almost zero frequency in plasma rest frame), it seems more correct to say that the energy is transferred gradually as the decay of the structures rather than periodically. If it is not the case, it is only necessary to show that the compressional component was not dominant. I think that it will be more reader-friendly and the physics easier to understand if the electromagnetic field is converted to the field-aligned coordinate system (toroidal, poloidal, and compressional components) in the entire discussion related to the ULF waves. Instead of Fig. 1a, I suggest plotting the three components of the magnetic field variation in the field-aligned coordinates and the three components of the electric field variation (=Ew?) in the field-aligned coordinates with two panels. If there is a possibility that the compressional component was dominant, it seems appropriate to cite a couple of papers on compressional ULF waves (structures) in addition to those on the other modes that have already been cited.
Thanks very much for the comments, and sorry that we did not catch this point in the previous review processes.
As suggested by the reviewer, we now plot in Fig. 1c the three components of the magnetic field variation (in the period range of 0.25-7 min) in a FAC system defined according to the local magnetic field averaged over 12:15-12:25 UT. (Please also see the ULF-wave electric fields in Fig. 1d, 1e, and Supplementary Fig. 1a  This observation is supported by a cross-wavelet analysis of them, which, as shown in Supplementary Fig. 1c and 1d, gives a correlation coefficient of ~0.75 and phase shift of ∘ at the period of the ULF waves (~3.4 min). As a result of the phase relationship, positive energy gain is generated. We note that the contribution from the radial component dominates the total energy gain. As shown in Supplementary Fig. 1e, the black curve, which represents the total energy gain, follows the red curve corresponding to the radial component well. On the other hand, Va and Ea are not well correlated (Fig. 1d). The corresponding cross-wavelet correlation coefficient is only ~0.5. Also, the contribution from the azimuthal component (the green curve in Supplementary Fig. 1e) to the total energy gain is generally smaller than that of the radial component. are not well correlated (CC<0.5). Also, their contribution to the is smaller than that of the radial component ( Supplementary Fig. 1e).

Comment 4
Is δEULF→i different from P? Although it is a critical parameter, there is no description of how it is calculated. Since there is no way to know which time intervals were used to derive the values, it is unlikely that the reader will be able to reproduce it. The significance of those values is also unclear. Since the parameters shown in the table are complex and the number of events has been reduced to only three, I think that it might be easy to understand for readers to show three additional supplementary figures in the same format (after update) as Fig. 1. If the table is kept as it is, I think it will be better to replace the components written in the ULF Field with those in the field-aligned coordinates (toroidal, poloidal, or compressional), and for δEULF→i, the time interval used for the calculation should be indicated in each added figure with the description in the figure caption. It may be worthwhile to add the events treated in the main text to the table.
We are very grateful to the reviewer for the comments. → denotes the average value of over corresponding time intervals.
Please note that, to avoid any potential uncertainty and ambiguity, we have removed the three supplementary events from the Supplementary Materials in the new version of the manuscript. Our main concern is that, unlike the cases shown in the main text, the ULF waves in these supplementary events are not monochromatic, making it very hard to obtain the ion energy gain related to the periodical EMIC-wave packets accurately. Therefore, we think it is better not to show these events. (We noted this issue when we were considering comment #1. We sincerely thank the reviewer for this comment.) Besides Supplementary Table 1, relevant discussion in the main text (e.g., "For example, we list another three similar events in Supplementary Table 1", lines 124-126) has also been removed.

Minor comments
Comment 5 Since it has changed to treat not only EMIC waves but also ULF waves in detail in this revision, the use of Ew, Ewave, Bwave, and fwave, etc. makes it difficult for readers to understand which wave they are related to. I suggest replacing them with descriptions (e.g., Ew_EMIC or Ew_ULF) that makes it easy to identify immediately which wave they are related to.
Thanks very much for the suggestion. We have revised the manuscript accordingly. Now, variables associated with ULF wave and EMIC wave are denoted with subscripts "ULF" and "EMIC", respectively. Please see the manuscript for detail.

Comment 6
Using E for both electric field and energy is confusing. The same is true for the use of f for PSD and frequency. The use of P for energy transfer is also slightly confusing with Power. I recommend improving on such representations. (I apologize for oversight in pointing this out in my previous review.) Thanks. All suggestions have been adopted. Now, "E", "W", "f" and "PSD" are used to represent the electric field, energy, frequency and PSDs. Also, instead of "P", now the ion energy gain is denoted by " / ", from which one can easily get the meanings.
I feel that the current revision of this paper, together with its supplementary material, has clarified many of the points raised. They now focus on two key events and improve and clarify definitions of the quantities analysed. This adds significant weight to their conclusions. I therefore feel it is suitable for publication.
Reviewer #3 (Remarks to the Author): I think that the authors addressed my suggestions adequately, and this manuscript can be accepted for publication in Nature Communications after a minor revision.
Minor comment Figure 1: I think that a line plot of wave intensity variation is easier to understand for readers than a power spectrum. It would be good to recover the line plot showing wave intensity variation, which shows a clear correlation with dw/dt and A, that was previously removed.

Response to Reviewer #1:
I feel that the current revision of this paper, together with its supplementary material, has clarified many of the points raised. They now focus on two key events and improve and clarify definitions of the quantities analyzed. This adds significant weight to their conclusions. I therefore feel it is suitable for publication.
We are very grateful to reviewer #1 for his/her continued efforts in evaluating this paper.

Response to Reviewer #3:
I think that the authors addressed my suggestions adequately, and this manuscript can be accepted for publication in Nature Communications after a minor revision.
We are very grateful to reviewer #3 for his/her continued efforts in evaluating this paper. We have carefully considered the comments shown below and revised the manuscript accordingly.
Minor comment Figure 1: I think that a line plot of wave intensity variation is easier to understand for readers than a power spectrum. It would be good to recover the line plot showing wave intensity variation, which shows a clear correlation with dw/dt and A, that was previously removed.
Thanks for the suggestion. We have recovered the line plot of wave intensity variation. Please find the panel h of the revised Fig. 1.